Grade 7 math

How to add and subtract negative numbers using the number line, why subtracting is the same as adding the opposite, and how to handle two signs in a row.

The sign rules for multiplying and dividing negatives, why two negatives make a positive, and how to handle several negative factors at once.

How to combine negative fractions and decimals across all four operations, why the integer sign rules carry over unchanged, and how to work multi-step problems in order.

How to convert between units by multiplying by a ratio equal to 1, why the unwanted unit cancels, and how to decide which way up the conversion factor goes.

How to tell whether two quantities are proportional from a table, graph or equation, find the constant of proportionality, and why the graph passes through the origin.

What a proportion is, how to solve one by cross multiplying, why cross multiplication works, and how to check whether two ratios form a proportion.

What a unit rate is, how to find one by dividing, how to use unit price to compare two deals, and the difference between a rate and a ratio.

How to find a sale price, add sales tax, and calculate a tip, using one multiplication instead of two steps — and why the order does not matter.

How to find what percent one number is of another: divide the part by the whole and multiply by 100, and how to tell which number is the whole.

How to find a percent increase or decrease, why the change is always measured against the original, and how to apply one in a single multiplication.

Three ways to find a percent of a number: convert to a decimal and multiply, use a fraction, or build it from 10% and 1% in your head.

Every percent word problem is one of three questions. How to tell which you have been asked, and how to solve each one, with worked examples.

How to use I = Prt to find simple interest, how to rearrange it for any missing letter, and why simple interest differs from compound interest.

What percent means, why it is out of one hundred, and how to move between a percent, a fraction and a decimal without memorizing three separate rules.

What makes two terms alike, how to collect them by adding their coefficients, why the variable part never changes, and how to move terms safely with their signs.

How to multiply across parentheses, why the area model explains it, how a negative outside the parentheses changes every sign, and how to factor by reversing the process.

How to turn a worded problem into an equation or inequality, what solving actually asks, which words signal each inequality sign, and how two quantities relate.

Solve one-step equations by doing the same inverse operation to both sides, with worked examples, common mistakes, and practice problems with full solutions.

Solve one-step inequalities the same way as equations, plus the one rule that changes: why the sign flips when you multiply or divide by a negative.

Solve two-step equations by undoing addition first and multiplication second, with worked examples, common mistakes, and practice problems with full solutions.

What probability means, how to calculate it for equally likely outcomes, why every probability sits between 0 and 1, and how experimental results differ from theory.

How to find the probability of two events happening together using organized lists, tables and tree diagrams, and how dependent events differ from independent ones.

Why a random sample can represent a whole population, what makes a sample biased, how to estimate a population value from one, and how to compare two groups fairly.

What complementary, supplementary, vertical and adjacent angles are, why each relationship holds, and how to use them to find a missing angle.

How to find the area of a circle from its radius or diameter, why the formula squares the radius, and the mistake of using the diameter instead.

How to find the circumference of a circle from its diameter or radius, what pi actually is, and how to work backwards from a known circumference.

Which sets of side and angle measurements pin down exactly one triangle, which allow many, and which allow none — and what flat shapes appear when a solid is sliced.

How to read a scale, convert between drawing and actual distances, find a scale factor, and why area scales by the square of the length factor.

What a net is, how unfolding a solid turns surface area into an addition of flat shapes, and how to find the surface area of a prism, cylinder and pyramid.